Definitions based on both the unit circle. In addition it touches on the philosophy of mathematics, commenting from time to time on the famous debate as to maths is discovered or invented. Inverse Trig Functions arcsin(x) range /2, /2 arctan(x) range (/2. Your pre-calculus learners will make use of this wonderful cheat sheet that summarizes all things trigonometric. From this follows what is probably the most beautiful and astonishing equation in all mathematics: e^i*pi + 1 = 0 or, re-expressed, e^i*pi = -1 This book attempts to chart the path which leads to that climax. In it he brings together the three most fundamental constants around which this book is based: e : central to logarithms, exponentials and the calculus, i : central to complex numbers, and pi : central to trigonometry (and much else). As Laplace said of him, 'He is the master of us all.' Euler's celebrated unification of trigonometry, complex numbers, and exponentials, described in his Introductio in Analysin Infinitorum (1744, published 1748), takes us to the climax of this book. In particular, we celebrate in this book the Swiss mathematician Leonhard Euler (pronounced 'oiler') (1707-1783), surely the greatest mathematician of the eighteenth century and unquestionably one of the greatest of all time. As a result, at whatever point a student leaves the course, he or she ought to have acquired a body of knowledge which has a definite beginning and progresses intelligibly towards a definite end. Where possible, it seeks to present mathematics in the order in which humankind discovered it, giving passing references to the discoverers of particular branches as it does so, and showing how one discovery led to the next. It differs from conventional texts primarily in terms of the sequence in which its material is presented, and in the connecting threads between topics. This book is intended for anyone who wants to learn, or refresh their understanding of, some of the basic elements of mathematics and how they relate to each other.

Trig cheat sheet for calculus